I doubt you would be asked "Why is Carbon-12 isotope used as the reference standard for atomic weight" in an exam, rather, you would just be asked to use Avogadro's constant
But anyways to answer your question: Carbon atoms have 6 protons, neutrons and electrons - and is defined as having 12 units on the relative atomic mass scale.
The 20th century (even now) do not possess technology great enough to measure specific atoms, rather, in large amounts of matter. Therefore, chemists established a reference standard for mass by using a more convenient method of measuring; namely grams.
This is known as the mole scale.
Chemists used various techniques to determine the number of atoms in exactly 12 g of carbon 12. That being Avogadro's constant of 6.022x10^23 atoms.
So essentially its just a nice number. 12C = 12g = 6.022x10^23 atoms/particles. Though he could have used any method of relativity, so yes he could have used any isotope he wanted, but he just used carbon and I don't think the numbers would have been nice if otherwise. Either way the periodic table would be very different if it were to be adapted to a different isotope.
Hope that helped.